Exponential stability for microtemperature Von Kármán beam with delay-time
Microtemperature von Kármán beam with delay-time
Resumo
In this paper, we consider a one-dimensional Von kármán beam with delay term coupled to a microtemperature equation. Under suitable assumptions on the weight of delay and a microtemperature effect we prove the exponential stability.
Downloads
Referências
Benabdallah, A. and Lasiecka, I. “Exponential decay rates for a full von K´arm´an system of dynamic thermoelasticity,” J. Differ. Equations 160, 51–93 (2000).
Benabdallah, A. and Teniou, D. “Exponential stability of a von Karman model with thermal effects,” Electron. J. Differ. Equations 7, 13 (1998).
Bouzettouta, L., & Abdelhak, D. Exponential stabilization of the full von K´arm´an beam by a thermal effect and a frictional damping and distributed delay. Journal of Mathematical Physics, 60(4), 041506, (2019).
Casas, P.S. and Quintanilla, R. ” Exponential stability in thermoelasticity with microtemperatures”, Int. J. Eng. Sci. 43 33–47. (2005).
Chirita, S. Ciarletta, M. and D’Apice,C. ”On the theory of thermoelasticity with microtemperatures”. J. Math. Anal. Appl. 397(1), 349–361, (2013).
Chueshov, l. and Lasiecka, l. Von Karman Evolution Equations, Springer Monographs in Mathematics (Springer, New York, p. xiv+766, well-posedness and long-time dynamics, 2010.
Djebabla, A. and Tatar, N- e. Exponential stabilization of the full Von K´arm´an beam by a thermal effect and a frictional damping, Georgian Math. J. 20, 427-438, (2013).
Favini, A. Horn, M. A. Lasiecka, l. and Tataru, D. Global existence, uniqueness and regularity of solutions to a von Karman system with nonlinear boundary dissipation, Differential Integral Equations 9, no. 2, 267–294, (1996).
Green, A. E. and Naghdi, P. M. A re-examination of the basic postulates of thermomechanics, Proc. Roy. Soc. London Ser. A 432, no. 1885, 171–194, (1991).
Green, A. E. and Naghdi, P. M. On undamped heat waves in an elastic solid, J.Thermal Stresses 15 , no. 2, 253–264, (1992).
Green, A. E. and Naghdi, P. M. Thermoelasticity without energy dissipation, J. Elasticity 31, no. 3, 189–208, (1991).
Green, A. E. and Naghdi, P. M. A unified procedure for construction of theories of deformable media. I. Classical continuum physics, II. Generalized continua, III. Mixtures of interacting continua, Proc. Roy. Soc. London Ser. A 448 (1995), no.1934, 335–356, 357–377, 379–388.
Hao J. and Wang, P. ” Exponential decay of solution to the viscoelastic porous-thermoelastic system of type III with boundary time-varying delay”. Math. Methods Appl. Sci. 39(13),3659–3668 (2016).
Horn, M. A. and Lasiecka, l. “Global stabilization of a dynamic von K´arm´an plate with nonlinear boundary feedback,” Appl. Math. Optim. 31, 57–84 (1995).
Lagnese, J. E. “Modelling and stabilization of nonlinear plates,” in Estimation and Control of Distributed Parameter Systems (Vorau, 1990), International Series of Numerical Mathematics (Birkh¨auser, Basel, 1991), Vol. 100, pp. 247–264.
Lagnese, J. E. and Leugering, G. Uniform stabilization of a nonlinear beam by nonlinear boundary feedback, J. Differential Equations 91, no. 2, 355–388, (1991).
Lesan, D. I.” A theory of thermoelastic materials with voids”, Acta Mech., vol. 60, no. 1–2, pp. 67–89, (1986).
Lesan, D. I. and Quintanilla, R. ”A theory of porous thermoviscoelastic mixtures”, J. Thermal Stresses, vol. 30, no. 7, pp. 693–714, (2007).
Liu, W. and Chen, M. ” Well-posedness and exponential decay for a porous thermoelastic system with second sound and a time-varying delay term in the internal feedback”. Contin. Mech. Thermodyn. 29, 731–746, (2017).
Puel, J.-P. and Tucsnak, M. BoundarystabilizationforthevonKarmanequations, SIAM J. Control Optim. 33, no. 1, 255–273, (1995).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
